Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference

TL;DR

This paper presents a data-driven, uncertainty-aware optimization framework for allocating vaccines during epidemics, using Gaussian process-based Bayesian inference to model parameter uncertainty in nonlinear epidemic models, leading to improved allocation strategies.

Contribution

It introduces a novel approach combining Gaussian process Bayesian inference with stochastic optimization for epidemic resource allocation, accommodating nonlinear ODE constraints and parameter uncertainty.

Findings

Accounting for parameter uncertainty improves vaccine allocation efficacy by 4-8%.

The method is flexible and applicable to various compartmental epidemic models.

Early-stage data-driven strategies significantly impact long-term epidemic outcomes.

Abstract

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.